For design of an electronic circuit or of a microelectromechanical system (MEMS), many physical parameters of constitutive components must be taken into account. In the case of an electronic circuit including several components, the physical parameters may correspond to the features of its constitutive transistors, resistors, and inductors, for example. In the case of a single electronic component such as an inductor, the physical parameters may correspond to the size of the inductor, to the properties of the material used to form the inductor, and to the properties of the materials close to the inductor, for example. For a microelectromechanical system, by way of example only, the physical parameters may correspond to the system dimensions and to the mechanical properties of the elements.
It is generally desirable to know the variation of physical properties which are characteristic of the electronic circuit or microelectromechanical system operation according to the physical parameters thereof. As an example, for an electronic circuit having several components, a physical property may be the consumption or the phase margin. For a single electronic component such as an inductor, a physical property may be the inductance value of the component or the quality factor. For a microelectromechanical system, a physical property may be the resonance frequency, or the cut-off frequency, or the sensitivity.
Determining the variation of a physical property according to physical parameters may be difficult. Indeed, it may be virtually impossible to determine a precise physical model of the operation of an electronic circuit or of a given microelectromechanical system based on equations of physics. Indeed, satisfactory physical models may not exist for certain ongoing physical phenomena, especially at very small scales. In this case, to know the variation of a physical property according to physical parameters, many tests would have to be carried out over all the variation ranges of the physical parameters. For reasons of time and cost, it is generally desirable to decrease the number of tests to a minimum. Only a few values of the physical property are then determined, which is insufficient to determine the full evolution of the physical property.
Even when physical models are available, the complexity of these models, especially due to the large number of physical parameters to be taken into account, makes it impossible to perform simulations over all the variations ranges of the physical parameters for reasons of time and cost, and only allows performing simulations for a few values of the physical property. Here again, this is insufficient to determine the full extent of the physical property.
To determine the extent of the physical property over all the variation ranges of the physical parameter, models are used, which are not obtained from physical equations but which only attempt to reproduce, as much as possible, the few available values of the physical property obtained by tests or simulations. Such models are said to be behavioral. They are generally simpler to implement and enable processes to simulate more easily the variation of the physical property over all the physical parameter variation ranges. An example of a behavioral model may correspond to a polynomial model.
Determining a behavioral model thus requires having values of the physical parameters and corresponding values of the physical property obtained by tests or simulations. Specific values of the physical parameters for which the corresponding value of the physical property is obtained by test or by simulation are generally called experiments or experiment points. The experiments altogether form what is called the experimental design.
A technical problem is to determine which experiments must be done to determine the behavioral model. Finding a solution to this technical problem is difficult, knowing that it is desirable for the number of experiments to be as small as possible to decrease the number of tests or simulations to be performed, and to have experiments which are as “representative” of the behavior of the electronic circuit or of the microelectromechanical system to better determine the behavioral model.
In the case of a behavioral model of polynomial type, there exist techniques for systematically determining, according to the selected polynomial model type, the optimum experimental design according to a given optimality criterion (D-optimality, G-optimality, etc.). An example of such a technique is described in the work entitled “La méthode des plans d'expérience—Optimisation du choix des essais & de l'interprétation des résultats” by J. Goupy, Editions Dunod, 1996. However, when the number of physical parameters is large, these techniques require determining a large number of experiments. It is then necessary to simplify the polynomial model or to limit the research to smaller variation ranges of the physical parameters to decrease the number of experiments.